In appliances of this nature, the cold water reservoir is generally arranged within the housing to obtain reduced size. However, in use, it is apparent that this type of appliance is inconvenient to use, particularly on the one hand when it is disposed on a very narrow working surface and, on the other hand, when the user has already placed the cooking chamber full of food on the housing before filling the reservoir with cold water. Thus, the operation of filling with water requires a certain skill on the part of the user because he must systematically withdraw the cooking chamber from the housing to have access to the cold water reservoir. This operation of filling thus requires careful attention of the user and greatly increases the period of time before starting the operation of the appliance. On the other hand, in the course of cooking, it requires great care and is dangerous to add water to prolong the production of steam.